HAL Id: hal-00702177
https://hal.archives-ouvertes.fr/hal-00702177
Submitted on 29 May 2012
HAL
is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire
HAL, estdestinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Smit h-prediction based Haptic Feedback Controller for Time Delayed Virtual Environments Systems
Hichem Arioui, Said Mammar, Tarek Hamel
To cite this version:
Hichem Arioui, Said Mammar, Tarek Hamel. A Smit h-prediction based Haptic Feedback Controller
for Time Delayed Virtual Environments Systems. American Control Conference, May 2002, Anchor-
age, United States. pp.4303-4309. �hal-00702177�
Delayed Virtual Environments systems
H.Arioui, S. Mammarand T. Hamel
Complex Systems Laboratory { Evry University
40, rue du Pelvoux, 91020 Evry Cedex, Frane
E-mail : arioui, smam,thamelemif.univ-evry.fr
Abstrat
InthispaperamodiedSmithpreditorforlinearde-
layedhaptiinteration ispresented. Theobjetiveis
to design afeedbak lawwhih ompensates thetime
delay by itssomehow elimination from the harater-
istiequation ofthelosed loopsystem. This method
isrobustwithin aertainsafepreditioninterval. The
appliabilityofSmithpreditorintheaseofhaptiin-
terationusingomputerhaptialgorithmsis shown.
1 Introdution
We are primarily onerned with stability analysis of
systems that involveshapti devies used for intera-
tivemanipulations within virtualenvironments(VE).
Ingure1ageneralshematiofsuhsystemsisshown.
Virtual Environment
Human Haptic
Interface
Computer Control Velocity
Force
Commands
Feedback
Communication Virtual Environment
Human Haptic
Interface
Computer Control Velocity
Force
Commands
Feedback Communication
Figure 1: Haptiinterationsystem
VE haptisystemsissimilar with someextend tothe
well known master-slave teleoperation systems. Tele-
operationsystemssynergistiallyombinehumansand
mahines and this man-mahine link is what makes
thempartiular. Inordertomaketheslaverobotrepli-
atesoperatordesiredtrajetoriesintheonehand,and
to onveythe Kinesthetislaverobot-environmentin-
terationas afeedbaktotheoperatorviathemaster
robotisystemintheotherhand. Abilateraloupling
ontrolshemewhihmakes,intheidealase,themas-
ter and the slave traking eah other is designed. As
forteleoperation,VE haptisprovideimportantinfor-
mation issued from syntheti virtual objets intera-
tionswithin theVE.However,as forteleoperation,it
is well known that small ommuniation delays may
trolmethods. Intheframeofteleoperation,Anderson
andSpong [1℄ haveproposed aontrol lawfor teleop-
eratorswithtimedelaybasedonpassivityandsatter-
ing theory [2℄. This method allows astable behavior
forany non-varyingtime delay. Niemeyerand Slotine
[3℄ elegantly reformulate Anderson and Spong's work
byintroduing\wavevariables"notiononthebasisof
network theory. Themajorproblem when usingwave
variables still, upto date, theperformanes degrada-
tionasthedelayinreases. Severalreentworksextend
theprevioustehniques forthe time varying delay, as
in thease ofInternet [4℄,suh as Stramigioli[5℄ and
Yokokojhi[6℄andfortheenhanementofperformanes
usingawavepreditor[7℄.
Other approahes are based on the H
1
optimal on-
troland-synthesis,Leung[8℄. Fiorini[9℄analyzesthe
stabilityofasimplePD-typestatefeedbakontroller
forateleoperationsystemoverInternet,usingstability
onditionsderivedfromaproposedLyapunovfuntion.
FortheuseofSmithpreditortostabilizealineartime
delayedsystem, several ontroller synthesis were pre-
sented. In [10℄, Smith and al. have proposed a delay
ompensation method whih uses amodel of thepro-
ess in the feedbak loop around aonventional on-
troller. Itis shown that usingthis tehniquethe time
delay an beeliminated from the harateristiequa-
tionofthe system. Other approahesbasedon Smith
preditor using state spae equations have been pro-
posedfortreatingtherobustnesstowardsinitialondi-
tionsproblemsand disturbanes[11℄ and[12℄. Never-
theless,Smith preditor hasneverbeenimplemented,
fromapureontrolpoint-of-view,ontimedelayedtele-
operationsystems. Thisisduetothefatthatitisnot
feasibleto predithazardousremoteenvironmentsbe-
havior. Indeed,it is diÆultto atuallypredit when
ontatwill our,theontat interationparameters
whenitours,theoperatorbehaviorandoperatorde-
sired trajetories, et. However, pratial implemen-
tations havebeenmade using various graphi predi-
tors i.e. a VE (augmented reality based vision feed-
bak, teleprogramming shemes, supervisory ontrol,
et.) anddisrepaniesreoverystrategies.
Thepaperis organizedas follows. Werst denethe
modelofthehaptiinteration: aposition-forebased
kinestheti feedbak sheme. We then briey review
thedenition ofSmithpreditorand solutionsforini-
tialonditionproblemsanddisturbanesproblems. In
thesamesetionwedisusstheappliabilityofthepre-
ditor in the ase of hapti interation. Insetion 4,
wedevelopaontrollerinnominalase. Finally,simu-
lationresultsonatual1DOFforefeedbakinterfae
ispresentedandresultsaboutrobustnessoftheontrol
shemearedropped.
2 PreviousWork in Hapti Simulation
InPreviousworksonhaptisystemshasmadetheas-
sumption that the operator and the virtual environ-
mentarepassive,fousingonotheraspetsofthesys-
tem toensure stable haptiinteration. Infat, most
of the proposed ontrol strategies are typially vari-
ous adaptations of the proposed bilateral ontrollers
developed for fore reeting teleoperation systems.
All thesestrategiesaretranslatedandadaptedforthe
VEhaptiinteratsontextmainly inadisreteform.
Sine Smith preditorshave notbeen investigated for
teleoperationsystems,to thebest authors knowledge,
thereseemsto benowork addressingtheirimplemen-
tationin theframe ofVE haptis. Moreover,thelim-
itations whih inhibit theuseof preditionforteleop-
erators do not hold in the VE haptis ontext sine,
ontatpreditionandinvolvedvirtualobjetsparam-
etersareknownthankstotheavailableomputerhap-
tis algorithms.
Adamsandal. [13℄presentedanapproahusingtheso
alled \virtual oupling" network between the hapti
devie and the held virtual objet. The virtual ou-
pling allows the environment design to be separated
from the sampled-data ontrol issues assoiated with
haptidisplay. Thoughthis solutionhasbeenalready
proposedintheontextofteleoperation[14℄. Themain
advantageof suh aontrol design isthat the param-
eterizationof thevirtualmehanismusedfor theou-
plingbetweenthehaptiinterfaeandthemanipulated
virtualobjetan be elaboratedso that thepassivity
ofthewholesystemispreservedusinglinearinteron-
netednetworkstheory.
Consideraonedegree-of-freedom(DOF)haptidisplay
shownin gure2withthehaptidevie M(s),virtual
ouplingC(z)andvirtualenvironmentE(z).
Iftheondition:
R e
1
C(z)
1 os(
6
ZOH(z))
R e(M(z))
jZOH(z)j (1)
holds,theunonditionalstabilityofthehaptiintera-
s e−sT
1− M ( s) 1s
Tz z−1
Tz z−1 )
( 1 z C
−1 z
) Tz
( z E
+
+
_ _
Fh
Vm Xm
Xc
Xe
Fe
Figure 2: Modelofone DOFhaptidisplay
tionissatised. Inotherwords,thehaptidisplayap-
pearspassive,asseenbytheoperator[13℄. Thehoie
oftheparametersofthevirtualouplingshouldsatisfy
someperformaneproperties.
IfweinteratwitharemotelyloatedVE(suhason-
urrentengineeringdesignsoftwareorsimplyashared
VE) the ommuniation hannel is then loated be-
tweenthevirtualouplingandthevirtualenvironment
asitisshownin thegure1. Inthisase,theommu-
niationtimedelaywillindubitablydestabilizethesys-
temsine the passivity of the systemis ompromised
and no longer preserved. One ould ompensate the
time delayby aglobal reformulationof the ontroller
usingpreviouslyitedteleoperationforereetingap-
proahes. Thesolutionproposedhere,andformulated
using Smith-based predition, onsists in keeping the
virtualouplingas aloal ontrollerand ompensates
theommuniationtimedelaybyaseparateVE-based
Smith predition-type ontrol. Thedetail of theon-
troller design is explained in setion 4. In order to
better understandtheproposed methodwewill reall
theSmithpreditionpriniple.
3 Smith preditionmethod
Considerthefollowingmono-variablesystemdesribed
by:
:
x(t) = Ax(t)+Bu(t )
y(t) = Cx(t)
(2)
x(0)=x
0
; u(h)=u
0
(h) h<0
where u is the ontrol input, x is the state variable,
y is the output, is the delay, and u
0
is the initial
funtion of theinput. A, B and C are onstant ma-
triesof appropriate dimensionsfor theproess. It is
assumed that ( A;B) is ontrollable and ( C ;A) is ob-
servable. The transferfuntion ofthelosed loopsys-
tem using astati unit feedbak relating the output,
y(t), to the desired input y (t) (see gure3) is given
Y(s)
Y
d (s)
=
C(sI A) 1
Be s
1+C(sI A) 1
Be s
wheresistheLaplaetransformvariable.Inthisequa-
tion,notethattheharateristiequationofthelosed
loopsystemontainsthetimedelayelementleadingto
aninnitenumberof eigenvalues. Controllinganin-
nite number of eigenvalues is not pratially feasible.
UsingSmithpreditionmethodthetimedelayelement
an be eliminated from the harateristi equation of
the losed loop system. The design problem for the
proesswithtimedelayan betransformedtotheone
withoutdelay.
G(s)e
-τsG(s) – G(s)e
-τs–
–
u y
y
dε
G(s)e
-τsG(s) – G(s)e
-τs–
–
u y
y
dε
Figure3: Smithpreditorbasedontrolarhiteture
In gure 3, " is the error, y
d
is the input signal, y is
theoutputsystemanduistheontrolsignal.
TheSmithpreditorontrolforsystem(2)isshownin
gure 3. The blok G(s)e s
, where G(s) = C(sI
A) 1
B, istheproessmodelwithoutdelay. Thefeed-
bakelementG(s) G(s)e s
isthenominalmodelof
the proess whih is assuming that is well identied.
Thetransferfuntion beomes:
Y(s)
Y
d (s)
=
C(sI A) 1
Be s
1+C(sI A) 1
B
Thesystemrepresentingbytheabovetransferfuntion
isstableunder someonditionsonA, B andC.
However,theSmithpreditorontrollerannothandle
thedisturbanesandnonzeroinitialonditionsasseen
in [11℄. A lose analysis of many improved shemes
(examples: Proess-ModelControl shemes[11℄,nite
spetrumassignmenttehniques[12℄showthattheyall
useinanexpliitorimpliitmannerapreditorofthe
state at time t+ in order to ahieve the ontrol of
the system (2). Unfortunately, in response to uner-
tain initial onditions or disturbanes, the predition
annot alwaysensureastable systemresponses. This
problem will notbe treatedin thispaper(see[15℄for
morethroughdevelopmentoftheproblem).
4 Controllerdesign based Smith preditor
Inthissetion,theSmithpreditionofthepreviousex-
ti interation will ontain a time delay between the
virtual oupling and the virtual environment in both
diretion as presented in gure 1 by the ommunia-
tionhannel. The transferfuntion ofthelosed loop
simplied delayed system beomes in the ontinuous
ase:
thetransferfuntionfrom F
h toF
e
isgivenby
F
h F
e e
s2
M(s)
s F
e e
s2
C(s)
e s1
E(s)=F
e
F
e (s)
F
h (s)
=
1
s
M(s)E(s)e s
1
1+e
s(1+2)
E(s) 1
s
M(s)+C(s)
Itisstatedlearlythattheobtainedlosedloop(when
ontatisourringbeauseinthefreemotionthesta-
bilityproblemisnotonsideredandthesystemisopen
loop) system has an innite eigenvalues beause the
timedelayelementispresentintheharateristiequa-
tion whih may imply the potential instability of the
system.
TheproposedsolutiontothisproblemisasimpleSmith
preditor based ontroller using the proess model of
the hapti display performing like afeedbak around
thevirtualenvironment. Thisisshownin gure4.
) ( ) 1 (
s C s sM
+
) (1 2
) ( )
1 ( − τ+τ
⋅
M s +C s e s s
) (s E
+
+ _
x
eF
e_
Figure4: Controllerdesign
Theresultingtransferfuntion oftheglobal systemis
astablehaptisimulationwithadelayedinput
F
e (s)
F
h (s)
= 1
s
M(s)E(s)e s
1
1+E(s) 1
s
M(s)+C(s)
(3)
Notethat thereis nodelayin theharateristiequa-
tion(3). Themainadvantageofthisontrol-predition
shemeistheuseoftheproessmodelofthehaptidis-
play only whih is -in almost ase-well know and its
parametersarewellidentied. Inotherwords,theuse
oftheontrollerbasedonSmith preditionis toelim-
inate the delayedresponse F
e
ofthe master part and
replae it with non-delayed response. The resultant
globalsystemisasysteminwhihthedelayisonlyin
5.1 NominalDesign
The hapti system simulation's harateristis are as
follows:
ThemasterpartisasingleDOFhaptiinterfae
allowingdisplaementsinasinglediretion. Itis
assumedthat thehaptiinterfaeisarigidstik
ofmassm=0:2KgmountedonaCCdiretdrive
atuatorforwhihweexperimentdierentvalues
of thevisous frition(b = 0:5 N:s
m
is a nominal
values).
TheforeF
e
isperformedwhenavirtualontat
ours inthevirtualenvironment(VE).
The Virtual Coupling Network is hosen to be
aPD-ontrollerC(s)= X(s)
F
e (s)
= 1
B
s+K
, itsrole
istoensureunonditionalstabilityundernotime
delay. K
=10 N
m andB
=10 N:s
m
areparameters
whihshould satisfyondition(1).
The VE is a virtual wall with stiness oeÆ-
ient K
e
= 1000 N
m
. When ollision ours,
thereeted fore obeysto Hook's law, that is:
F
e
=(x
wall x
e )K
e
=xK
e , x
wall isthe
positionofthewall.
Delaysaretakentobe
1
=2
2
=1se(nominal
values).
0 2 4 6 8 10 12 14 16 18
-2000 -1500 -1000 -500 0
Master Position
Slave position
Masterposition(m)
Time (sec)
Figure5: Unstablebehaviorofhaptisimulation(multi-
pleontat)
Simulation results are shown in gures 5, where the
hapti simulation present a unstable behaviordue to
transmissiondelays(
1
;
2 ).
Now, we apply the developed predition-based on-
troller (with nominal parameters), we obtain as ex-
onstrained motion) between master and slave is in-
verselyproportionaltovisousfritionoeÆientofthe
haptiinterfaeband delay
2
in ontrol F
e
. Inother
words,theollisiondetetionintheVEandtheexeu-
tionoftheommanddue to theollisiontheoperator
ontinuetomove.Inthefreemotion,theslaveposition
isequalto masterdelayedposition (delayequalto
1 )
gure6.
0 5 10 15 20 25 30 35 40
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
Time (sec)
Masterposition(m)
Master position
Position difference while contact made
slave position Slave velocity VE force
Fh
Free motionConstrained Free motion
motion Free motion
Master velocity
Figure6: StabilizationwithSmith-preditorController
Figure6showsthemasterpositionandtheprogressive
attenuation ofthe unavoidabledisrepany (whatever
the ontroller is) of the master and virtual positions
during the ontat. The explanation is quite simple :
Atthebeginning,themasterspeedinreasesastheap-
plied operator fore (F
h
)inreases.When theontat
ismade(v
m
=0:1mse 1
;x
m
=0:34m),weannotie
that the master speed drops toward zero, then on-
tinue to derease. Beause of the operator speed and
thebakwarddelay, theerror(the penetration) is ex-
atly = 0:007m for the rst ontat, whih means
that theoperator feelsthe foreof theVE (F
e ) when
x
m
= 0:34m. The onstraint on slave position is re-
speted(0:2monthegure6)duetothehighstiness
ofthevirtualwall.TheVE reationfore (F
e
)iswell
fed andounterparts,to someextent, theapplied F
h .
Thelatterinreasestoamaximumanddereases,this
behavior is desired, as we took asin funtion for F
h .
Onean notie thegood delityin fore andveloity
restitution(asthereisnoerrorbetweenthemasterand
slaveveloitiesduringfreemotions). Whentheontat
brakes, the remote position mathes the desired one
after adelay
1
. Severalsimulations whereperformed
withvarious ontatbehavior(multiple ontats, and
various VE stiness), the results show a good stable
sheme
A future work will ontainthroughdevelopmentsand
explanationonerningtherobustnessissuesduetoer-
rorestimationofthemastermodelandwehaveextend
thismethodwhihbeamefreefromthedelayestima-
tion. Intheallowedspaeweonlypresentsomeresults
onerning system behaviordue to errors in the esti-
mationinthedelayvalue.
0 5 10 15 20 25 30 35 40
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
Time (sec)
Masterposition(m)
Master position
slave position Slave velocity VE force
Free motion Constrained Free motion
motion Free motion
Master velocity
Figure7:Robustnessofontrollerdutomismathdelays
=50ms
Figure 7shows astable behaviorof the hapti inter-
ationwhen =
1
+
2
2℄0;0:05℄s(where
i
istheerrorestimationbetweenthetransmissiondelay
i
and thevirtualdelayusedbytheSmithontroller),
however, it an be notied that small osillationsap-
pear in virtual environment fore or veloities whih
may deteriorate system performanes. It should be
noted, that same osillations appear when error esti-
mationinmodel ofthehaptiinterfaeisonsidered.
0 5 10 15 20 25 30 35 40
-0.4 -0.2 0 0.2 0.4 0.6
Time (sec)
Masterposition(m)
Master position
slave position
Slave velocity VE force
Free motion Constrained
motion Free motion
Master velocity
-0.3 -0.1 0.1 0.3 0.5
Figure 8: Robustness of ontroller due to mismath in
modelestimationm=0:045kg
sidered. Figure 8showsastable behaviordue to per-
turbationsinmodelestimationofhaptiinterfaeusing
in Smith preditor Controller, onsidering errors only
in masse, the margin giving by Rouhe's Theorem is
jmj45g (see[?℄for morethroughdevelopmentof
therobustnessproblem).
6 Conlusion
In this paper, a ontroller stabilising delayed hapti
feedbak system and fore feedbak teleoperators has
been presented. The originality and the main idea of
thisworkistheinvestigationofaSmith-likepredition
withintheremote site(i.e. slaverobot site forteleop-
erationase,orinthesimulationenginewithinremote
VE).Theproposedontrollerhasbeenproventostabi-
lizeforefeedbakinterationforimportantdelaysand
dierent master to remote transmission delays. Only
themodelofthemasterhaptiinterfaeisneeded,and
in mostasesthismodelis available. Indeedtheon-
trollerguaranteesthestabilityof thesystembut gen-
eratesanonedesirablestatitrakingerror.Theon-
trolleris also robustto small systemparametersu-
tuations.Thedevelopmentofthesolutiontothestati
errorwithathoroughrobustnessanalysisarepresented
inanotherompanionpaper.
7 Aknowledgment
WewouldliketoexpressourgratitudetoHabibaDALI
forfruitfuldisussionandherontribution.
Referenes
[1℄ R.J.AndersonandM.W. Spong, \Bilateralon-
trolofteleoperatorswithtimedelay", IEEE Transa-
tions On Automati Control, vol. 34, no. 5, pp. 494{
501,May1989.
[2℄ C.A.DesoerandM.Vidyasagar, \FeedbakSys-
tems: Input-Output Properties", Aademi Press,
1975.
[3℄ G.NiemeyerandJ.J.Slotine,\UsingWaveVari-
ablesforsystem Analysis andRobot Control", IEEE
InternationalConfereneonRobotisandAutomation,
pp.1619{1625,April1997, Albuquerque,NewMexio.
[4℄ G. Niemeyer and J.J. Slotine, \Towardsfore-
ReetingTeleoperationovertheInternet", IEEE In-
ternational Conferene on Robotis and Automation,
pp.1909{1915,May1998, Leuven,Belgium.
[5℄ S. Stramigioli,A. V.D.Shaft, and B.Mashke,
\Geometri Sattering in tele-manipulation of port
